Nearly all communication system relies on some form of error control for managing errors that may occur due to noise and other factors during transmission of information through a communication channel. These communications systems can include satellite systems, fiber-optic systems, cellular systems, and radio and television broadcasting systems. Efficient error control schemes implemented at the transmitting end of these communications systems have the capacity to enable the transmission of data including audio, video, text, etc. with very low error rates within a given signal-to-noise ratio (SNR) environment. Powerful error control schemes also enable a communication system to achieve target error performance rates in environments with very low SNR, such as in satellite and other wireless systems where noise is prevalent and high levels of transmission power are costly, if even feasible.
Thus, a broad class of powerful error control schemes that enable reliable transmission of information have emerged including convolutional codes, low density parity check (LDPC) codes, and turbo codes. Both LDPC codes as well as some classes of turbo codes have been successfully demonstrated to approach near the theoretical bound (i.e., Shannon limit). Although long constraint length convolutional codes can also approach the Shannon limit, decoder design complexity prevents practical, wide spread adoption. LDPC codes and turbo codes, on the other hand, can achieve low error rates with lower complexity decoders. Consequently, these codes have garnered significant attention.
Code rate is an important factor that has a significant effect on the error performance of the code. The choice of which code rate to operate, in turn, depends on the SNR of the environment in which the codes will be deployed. Traditionally, low SNR environments require the use of low code rates (i.e., more redundancy), whereas high SNR environments can enable the utilization of higher code rates. There is a continual challenge to devise codes that edge closer to the Shannon limit, while minimizing complexity.
Based on the foregoing, there is a need for generating low rate codes for use within various types of communication systems.